(a) A particular household uses a 1.8 -k W heater 2.0 h / day ( "on " time) four 100-W lightbulb

step 1 We'll start by calculating the consumption of each appliance. Starting with the heater, I have 1

(a) A particular household uses a 1.8 -k W heater 2.0 h /...

(a) A particular household uses a 1.8 -k $\mathrm{W}$ heater 2.0 $\mathrm{h} / \mathrm{day}$ $($ "on " time) four $100-\mathrm{W}$ lightbulbs $6.0 \mathrm{h} / \mathrm{day}, \mathrm{a} 3.0 \mathrm{-k} \mathrm{W}$ electric stove element for a total of 1.0 $\mathrm{h} / \mathrm{day}$ , and miscellaneous power amounting to 2.0 $\mathrm{kWh} / \mathrm{day}$ . If electricity costs $\$ 0.105$ per kWh, what will be their monthly bill $(30 \mathrm{d})$ ? (b) How much coal (which produces 7500 $\mathrm{kcal} / \mathrm{kg}$ ) must be burned by a 35$\%$ -efficient power plant to provide the yearly needs of this household?

(a) A particular household uses a 1.8 -k $\mathrm{W}$ heater 2.0 $\mathrm{h} / \mathrm{day}$ $($ "on " time) four $100-\mathrm{W}$ lightbulbs $6.0 \mathrm{h} / \mathrm{day}, \mathrm{a} 3.0 \mathrm{-k} \mathrm{W}$ electric stove element for a total of 1.0 $\mathrm{h} / \mathrm{day}$ , and miscellaneous
power amounting to 2.0 $\mathrm{kWh} / \mathrm{day}$ . If electricity costs $\$ 0.105$ per kWh, what will be their monthly bill $(30 \mathrm{d})$ ? (b) How much coal (which produces 7500 $\mathrm{kcal} / \mathrm{kg}$ ) must be burned by a 35$\%$ -efficient power plant to provide the yearly needs of this household?

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Key Concepts

Thermal Efficiency in Power Plants

Thermal efficiency refers to the fraction of energy contained in a fuel that is converted into electrical energy. Understanding this concept is crucial when calculating how much fuel is necessary to deliver a desired amount of electrical energy, because losses during conversion must be considered.

Fuel Energy Content

Fuel energy content, such as the number of kilocalories per kilogram, indicates how much energy is stored in a given mass of fuel. This concept is important when converting overall energy needs into a required quantity of fuel, especially when working with fuels like coal.

Power and Energy Units

This concept involves understanding the difference between power and energy. Power (measured in watts or kilowatts) is the rate at which energy is used, while energy (measured in kilowatt-hours, kWh) is the total amount of work done over time. A clear grasp of these units is key for converting usage times into energy consumption figures.

Electrical Energy Consumption and Cost Calculation

Determining electrical energy consumption involves multiplying the power rating of devices by the time they are used, yielding energy in kWh. This calculation is fundamental when estimating electricity costs, as the total consumption is multiplied by the cost per kWh to derive the total bill.

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